Exact Dynamics of Multicomponent Bose-Einstein Condensates in Optical Lattices in One, Two and Three Dimensions

TL;DR

This paper derives exact, stable solutions for multicomponent Bose-Einstein condensates in optical lattices across one to three dimensions, revealing complex vortex and flow patterns in these quantum systems.

Contribution

It provides the first comprehensive set of closed-form solutions for multicomponent BECs in optical lattices, including stability analysis and diverse dynamical states.

Findings

Exact stationary and nonstationary solutions found

Vortex-anti-vortex arrays and inter-component flow modes identified

Several solutions shown to be stable through numerical simulations

Abstract

Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-anti-vortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.